I'm just going through this process at the moment but in 6mm. The thinking is still relevant for you I believe. I'm no resident expert, but I'm bored so I've played with the numbers for you. The alternative is what the Mrs has on the telly, which isn't good
I started by looking at the max range I wanted to shoot over. Call it 300m. In my experience TSX/TTSX/GMX bullets really need to have a TV of 2400 fps to expand efficiently and reliably - I know the manufacturers say it's lower than that but that's not my experience of that of many others - maintaining velocity is key to making copper bullets reliable. To work out the MV you need to achieve that 2400 fps TV you need to factor in the BC of the bullet.
Take your .308 with a 130 TTSX. If you can launch it at 3250 fps you will get 2400 fps at 300m. Look at the 26" barrel velocity Barnes claim on their ammunition and it's 3150 fps. So that's not going to work. The range limit with a 26" barrel will be about 260m. If you want to run a 22" barrel the velocity will drop to around 3000 fps and effective range will be down to about 220m.
Run the numbers again with a 150gr TTSX and they claim a MV of 2900 fps with a 26" barrel, probably down to around 2750 fps with a 22" barrel. Plug in the numbers and your effective range with the 22" is around 180m if you want to maintain your 2400 fps.
Alternatively, the most effective is likely to be the 110gr, but I don't think you could find that as factory loaded ammunition. That should get launched at around 3300/3350 fps and will still carry 2400 fps at 300m.
In terms of twist rates, the stability calculator says you will run the standard 12 twist with the 110's and 130's, 150's will need 11. The 165's your currently running should be at 10 twist.
I've shot quite a few deer with 7mm 120 TTSX at 3400 fps and 6.5mm 100 TTSX. The 7mm were mainly Red and Sika, the 6.5mm Fallow and Roe and a few red hinds. I found them to be a very reliable and effective bullet, quick killing and much less carcass damage than traditional lead bullets. I'm confident enough with them to be looking at a 6mm at the moment to shoot Fallow and Roe with the 80 TTSX. I wouldn't hesitate to use the 130gr TTSX in 30 cal on Red, but I would keep barrel length to at least 24" and limit range to 250m.